Abstract: In this paper, the irregular sphere gravitational potential is given based on adapting to a tri-axial ellipsoid model of a small body, and the spacecraft orbital dynamics equation around a small body is established. According to the integral Jacobi constant, the spacecraft zero-velocity curves in the vicinity of the asteroid are described and feasible motion regime is analyzed. Limited condition and periapsis radius corresponding to different eccentricity against impact surface are presented. Perturbation solutions of mean orbit elements are used. Effect of asteroid oblateness and ellipticity is analyzed. Lagrange perturbation equations based on mean orbit elements are used, a few partially frozen orbits are given, and the stability of frozen orbits is analyzed.

Key words: slowly rotating small body, zero-velocity curve, frozen orbit, orbit stability